If the mail does not arrive at your gmail account, then you should see a reason why in /var/log/maillog . The most common reason that I see is that the host does not know how to route mail to the outside world, or does not have a Smarthost configured in /etc/mail/sendmail.cf

This will work, but you may have to set parameter append_at_myorigin=no in main.cf in case myorigin is set. Otherwise if you are sending locally to "root" postfix by default will append myorigin value to the domain part of the recipient.